Step 1: Grasp Graham's Law of Diffusion.
Graham's law states that a gas's diffusion rate is inversely proportional to the square root of its molar mass:
\[
\text{Rate} \propto \frac{1}{\sqrt{M}}
\]
where \( M \) represents the gas's molar mass.
Step 2: Contrast the molar masses of the gases.
- \( \text{H}_2 \) molar mass: \( 2 \, \text{g/mol} \).
- \( \text{O}_2 \) molar mass: \( 32 \, \text{g/mol} \).
- \( \text{N}_2 \) molar mass: \( 28 \, \text{g/mol} \).
- \( \text{CO}_2 \) molar mass: \( 44 \, \text{g/mol} \).
Step 3: Ascertain the diffusion rate.
Given that the diffusion rate is inversely proportional to the square root of the molar mass, the gas with the smallest molar mass will diffuse most rapidly.
Of the listed gases, \( \text{H}_2 \) possesses the lowest molar mass, thus exhibiting the highest diffusion rate.
Answer: Consequently, \( \text{H}_2 \) will exhibit the highest diffusion rate.